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Long Short-Term Memory Recurrent Neural Network Architectures

for Large Scale Acoustic Modeling

Haşim Sak, Andrew Senior, Françoise Beaufays

Google, USA

Abstract task of acoustic modeling.

LSTM and conventional RNNs have been successfully ap-
Long Short-Term Memory (LSTM) is a specific recurrent neu- plied to various sequence prediction and sequence labeling
ral network (RNN) architecture that was designed to model tem- tasks. In language modeling, a conventional RNN has ob-
poral sequences and their long-range dependencies more accu- tained significant reduction in perplexity over standard n-gram
rately than conventional RNNs. In this paper, we explore LSTM models [6] and an LSTM RNN model has shown improve-
RNN architectures for large scale acoustic modeling in speech ments over conventional RNN LMs [7]. LSTM models have
recognition. We recently showed that LSTM RNNs are more been shown to perform better than RNNs on learning context-
effective than DNNs and conventional RNNs for acoustic mod- free and context-sensitive languages [8]. Bidirectional LSTM
eling, considering moderately-sized models trained on a single (BLSTM) networks that operate on the input sequence in both
machine. Here, we introduce the first distributed training of directions to make a decision for the current input have been
LSTM RNNs using asynchronous stochastic gradient descent proposed for phonetic labeling of acoustic frames on the TIMIT
optimization on a large cluster of machines. We show that a speech database [9]. For online and offline handwriting recog-
two-layer deep LSTM RNN where each LSTM layer has a lin- nition, BLSTM networks used together with a Connectionist
ear recurrent projection layer can exceed state-of-the-art speech Temporal Classification (CTC) layer and trained from unseg-
recognition performance. This architecture makes more effec- mented sequence data, have been shown to outperform a state-
tive use of model parameters than the others considered, con- of-the-art Hidden-Markov-Model (HMM) based system [10].
verges quickly, and outperforms a deep feed forward neural net- Similar techniques with a deep BLSTM network have been
work having an order of magnitude more parameters. proposed to perform grapheme-based speech recognition [11].
Index Terms: Long Short-Term Memory, LSTM, recurrent BLSTM networks have also been proposed for phoneme predic-
neural network, RNN, speech recognition, acoustic modeling. tion in a multi-stream framework for continuous conversational
speech recognition [12]. In terms of architectures, following
1. Introduction the success of DNNs for acoustic modeling [13, 14, 15, 16], a
deep BLSTM RNN combined with a CTC output layer and an
Speech is a complex time-varying signal with complex cor- RNN transducer predicting phone sequences has been shown to
relations at a range of different timescales. Recurrent neural reach state-of-the-art phone recognition accuracy on the TIMIT
networks (RNNs) contain cyclic connections that make them database [17].
a more powerful tool to model such sequence data than feed-
Deep BLSTM RNNs have recently been shown to per-
forward neural networks. RNNs have demonstrated great suc-
form better than DNNs in the hybrid speech recognition ap-
cess in sequence labeling and prediction tasks such as handwrit-
proach [2]. Using the hybrid approach, we have recently shown
ing recognition and language modeling. In acoustic modeling
that an LSTM architecture with a recurrent projection layer
for speech recognition, however, where deep neural networks
outperforms DNNs and conventional RNNs for large vocabu-
(DNNs) are the established state-of-the-art, recently RNNs have
lary speech recognition, considering moderately-sized models
received little attention beyond small scale phone recognition
trained on a single machine [3]. In this paper, we explore LSTM
tasks, notable exceptions being the work of Robinson [1],
RNN architectures for large-scale acoustic modeling using dis-
Graves [2], and Sak [3].
tributed training. We show that a two-layer deep LSTM RNN
DNNs can provide only limited temporal modeling by op- where each LSTM layer has a linear recurrent projection layer
erating on a fixed-size sliding window of acoustic frames. They outperforms a strong baseline system using a deep feed-forward
can only model the data within the window and are unsuited to neural network having an order of magnitude more parameters.
handle different speaking rates and longer term dependencies.
By contrast, recurrent neural networks contain cycles that feed
the network activations from a previous time step as inputs to 2. LSTM Network Architectures
the network to influence predictions at the current time step. 2.1. Conventional LSTM
These activations are stored in the internal states of the network
which can in principle hold long-term temporal contextual in- The LSTM contains special units called memory blocks in the
formation. This mechanism allows RNNs to exploit a dynami- recurrent hidden layer. The memory blocks contain memory
cally changing contextual window over the input sequence his- cells with self-connections storing the temporal state of the net-
tory rather than a static one as in the fixed-sized window used work in addition to special multiplicative units called gates to
with feed-forward networks. In particular, the Long Short-Term control the flow of information. Each memory block in the orig-
Memory (LSTM) architecture [4], which overcomes some mod- inal architecture contained an input gate and an output gate.
eling weaknesses of RNNs [5], is conceptually attractive for the The input gate controls the flow of input activations into the
input input input input



it ot recurrent recurrent


ct mt yt LSTM

g cell h
xt rt (a) LSTM
output LSTM
output (c) LSTMP
(b) DLSTM recurrent
LSTM memory blocks

Figure 1: LSTMP RNN architecture. A single memory block is
shown for clarity.

Figure 2: LSTM RNN architectures.

memory cell. The output gate controls the output flow of cell
activations into the rest of the network. Later, the forget gate
was added to the memory block [18]. This addressed a weak- instant. Therefore, the depth in deep LSTM RNNs has an ad-
ness of LSTM models preventing them from processing contin- ditional meaning. The input to the network at a given time step
uous input streams that are not segmented into subsequences. goes through multiple LSTM layers in addition to propagation
The forget gate scales the internal state of the cell before adding through time and LSTM layers. It has been argued that deep
it as input to the cell through the self-recurrent connection of layers in RNNs allow the network to learn at different time
the cell, therefore adaptively forgetting or resetting the cell’s scales over the input [20]. Deep LSTM RNNs offer another
memory. In addition, the modern LSTM architecture contains benefit over standard LSTM RNNs: They can make better use
peephole connections from its internal cells to the gates in the of parameters by distributing them over the space through mul-
same cell to learn precise timing of the outputs [19]. tiple layers. For instance, rather than increasing the memory
An LSTM network computes a mapping from an input size of a standard model by a factor of 2, one can have 4 lay-
sequence x = (x1 , ..., xT ) to an output sequence y = ers with approximately the same number of parameters. This
(y1 , ..., yT ) by calculating the network unit activations using results in inputs going through more non-linear operations per
the following equations iteratively from t = 1 to T : time step.

it = σ(Wix xt + Wim mt−1 + Wic ct−1 + bi ) (1) 2.3. LSTMP - LSTM with Recurrent Projection Layer
ft = σ(Wf x xt + Wf m mt−1 + Wf c ct−1 + bf ) (2)
The standard LSTM RNN architecture has an input layer, a re-
ct = ft ct−1 + it g(Wcx xt + Wcm mt−1 + bc ) (3) current LSTM layer and an output layer. The input layer is con-
ot = σ(Wox xt + Wom mt−1 + Woc ct + bo ) (4) nected to the LSTM layer. The recurrent connections in the
mt = ot h(ct ) (5) LSTM layer are directly from the cell output units to the cell
input units, input gates, output gates and forget gates. The cell
yt = φ(Wym mt + by ) (6) output units are also connected to the output layer of the net-
work. The total number of parameters N in a standard LSTM
where the W terms denote weight matrices (e.g. Wix is the ma-
network with one cell in each memory block, ignoring the bi-
trix of weights from the input gate to the input), Wic , Wf c , Woc
ases, can be calculated as N = nc × nc × 4 + ni × nc × 4 +
are diagonal weight matrices for peephole connections, the b
nc × no + nc × 3, where nc is the number of memory cells
terms denote bias vectors (bi is the input gate bias vector), σ is
(and number of memory blocks in this case), ni is the number
the logistic sigmoid function, and i, f , o and c are respectively
of input units, and no is the number of output units. The com-
the input gate, forget gate, output gate and cell activation vec-
putational complexity of learning LSTM models per weight and
tors, all of which are the same size as the cell output activation
time step with the stochastic gradient descent (SGD) optimiza-
vector m, is the element-wise product of the vectors, g and h
tion technique is O(1). Therefore, the learning computational
are the cell input and cell output activation functions, generally
complexity per time step is O(N ). The learning time for a net-
and in this paper tanh, and φ is the network output activation
work with a moderate number of inputs is dominated by the
function, softmax in this paper.
nc × (4 × nc + no ) factor. For the tasks requiring a large
number of output units and a large number of memory cells to
2.2. Deep LSTM store temporal contextual information, learning LSTM models
As with DNNs with deeper architectures, deep LSTM RNNs become computationally expensive.
have been successfully used for speech recognition [11, 17, 2]. As an alternative to the standard architecture, we proposed
Deep LSTM RNNs are built by stacking multiple LSTM lay- the Long Short-Term Memory Projected (LSTMP) architec-
ers. Note that LSTM RNNs are already deep architectures in ture to address the computational complexity of learning LSTM
the sense that they can be considered as a feed-forward neu- models [3]. This architecture, shown in Figure 1 has a separate
ral network unrolled in time where each layer shares the same linear projection layer after the LSTM layer. The recurrent con-
model parameters. One can see that the inputs to the model nections now connect from this recurrent projection layer to the
go through multiple non-linear layers as in DNNs, however the input of the LSTM layer. The network output units are con-
features from a given time instant are only processed by a sin- nected to this recurrent layer. The number of parameters in this
gle nonlinear layer before contributing the output for that time model is nc ×nr ×4+ni ×nc ×4+nr ×no +nc ×nr +nc ×3,
instructions. We implemented activation functions and gradi-
Table 1: Experiments with LSTM and LSTMP RNN architec- ent calculations on matrices using SIMD instructions to benefit
tures showing test set WERs and frame accuracies on devel- from parallelization.
opment and training sets. L indicates the number of layers,
We use the truncated backpropagation through time (BPTT)
for shallow (1L) and deep (2,4,5,7L) networks. C indicates the
learning algorithm [22] to compute parameter gradients on short
number of memory cells, P the number of recurrent projection
subsequences of the training utterances. Activations are for-
units, and N the total number of parameters.
ward propagated for a fixed step time Tbptt (e.g. 20). Cross
C P Depth N Dev Train WER entropy gradients are computed for this subsequence and back-
(%) (%) (%) propagated to its start. For computational efficiency each thread
840 - 5L 37M 67.7 70.7 10.9 operates on subsequences of four utterances at a time, so matrix
440 - 5L 13M 67.6 70.1 10.8 multiplies can operate in parallel on four frames at a time. We
600 - 2L 13M 66.4 68.5 11.3 use asynchronous stochastic gradient descent (ASGD) [23] to
385 - 7L 13M 66.2 68.5 11.2 optimize the network parameters, updating the parameters asyn-
750 - 1L 13M 63.3 65.5 12.4 chronously from multiple threads on a multi-core machine. This
effectively increases the batch size and reduces the correlation
6000 800 1L 36M 67.3 74.9 11.8 of the frames in a given batch. After a thread has updated the
2048 512 2L 22M 68.8 72.0 10.8 parameters, it continues with the next subsequence in each utter-
1024 512 3L 20M 69.3 72.5 10.7 ance, preserving the LSTM state, or starts new utterances with
1024 512 2L 15M 69.0 74.0 10.7 reset state when one finishes. Note that the last subsequence
800 512 2L 13M 69.0 72.7 10.7 of each utterance can be shorter than Tbptt but is padded to the
2048 512 1L 13M 67.3 71.8 11.3 full length, though no gradient is generated for these padding
This highly parallel single machine ASGD framework de-
where nr is the number of units in the recurrent projection layer. scribed in [3] proved slow for training models of the scale we
In this case, the model size and the learning computational com- have used for large scale ASR with DNNs (many millions of
plexity are dominated by the nr × (4 × nc + no ) factor. Hence, parameters). To scale further, we replicate the single-machine
this allows us to reduce the number of parameters by the ratio workers on many (e.g. 500) separate machines, each with three,
. By setting nr < nc we can increase the model memory synchronized, computation threads. Each worker communi-
(nc ) and still be able to control the number of parameters in the cates with a shared, distributed parameter server [23] which
recurrent connections and output layer. stores the LSTM parameters. When a worker has computed the
With the proposed LSTMP architecture, the equations for parameter gradient on a minibatch (of 3 × 4 × Tbptt frames), the
the activations of network units change slightly, the mt−1 acti- gradient vector is partitioned and sent to the parameter server
vation vector is replaced with rt−1 and the following is added: shards which each add the gradients to their parameters and re-
rt = Wrm mt (7) spond with the new parameters. The parameter server shards
aggregate parameter updates completely asynchronously. For
yt = φ(Wyr rt + by ) (8) instance, gradient updates from workers may arrive in different
where the r denote the recurrent unit activations. orders at different shards of the parameter server. Despite the
asynchrony, we observe stable convergence, though the learn-
2.4. Deep LSTMP ing rate must be reduced, as would be expected because of the
increase in the effective batch size from the greater parallelism.
Similar to deep LSTM, we propose deep LSTMP where multi-
ple LSTM layers each with a separate recurrent projection layer
are stacked. LSTMP allows the memory of the model to be in- 4. Experiments
creased independently from the output layer and recurrent con- We evaluate and compare the performance of LSTM RNN ar-
nections. However, we noticed that increasing the memory size chitectures on a large vocabulary speech recognition task – the
makes the model more prone to overfitting by memorizing the Google Voice Search task. We use a hybrid approach [24]
input sequence data. We know that DNNs generalize better to for acoustic modeling with LSTM RNNs, wherein the neural
unseen examples with increasing depth. The depth makes the networks estimate hidden Markov model (HMM) state posteri-
models harder to overfit to the training data since the inputs ors. We scale the state posteriors by the state priors estimated
to the network need to go through many non-linear functions. as the relative state frequency from the training data to obtain
With this motivation, we have experimented with deep LSTMP the acoustic frame likelihoods. We deweight the silence state
architectures, where the aim is increasing the memory size and counts by a factor of 2.7 when estimating the state frequencies.
generalization power of the model.
4.1. Systems & Evaluation
3. Distributed Training: Scaling up to
All the networks are trained on a 3 million utterance (about
Large Models with Parallelization 1900 hours) dataset consisting of anonymized and hand-
We chose to implement the LSTM RNN architectures on multi- transcribed utterances. The dataset is represented with 25ms
core CPU rather than on GPU. The decision was based on frames of 40-dimensional log-filterbank energy features com-
CPU’s relatively simpler implementation complexity, ease of puted every 10ms. The utterances are aligned with a 85 million
debugging and the ability to use clusters made from commod- parameter DNN with 14247 CD states. The weights in all the
ity hardware. For matrix operations, we used the Eigen matrix networks are initialized to the range (-0.02, 0.02) with a uni-
library [21]. This templated C++ library provides efficient im- form distribution. We try to set the learning rate specific to a
plementations for matrix operations on CPU using vectorized network architecture and its configuration to the largest value
70 c800_r512x2 c800_r512x2
72 c440x5
c600x2 c600x2
68 c385x7 c385x7
c750 c750
Frame Accuracy (%)

Frame Accuracy (%)

64 66

62 64

600 20 40 60 80 100 620 20 40 60 80 100

Training Time (hours) Training Time (hours)
(a) Held-out data. (b) Training data.

Figure 3: Frame accuracy vs training time.

that results in a stable convergence. As a result, the learning performance improvements.

rates for stable convergence of different networks range from Figure 3 compares the frame accuracies on training and
5e-06 to 1e-05. The learning rates are exponentially decayed held-out sets for various LSTM and LSTMP architectures. The
during training. With the correct learning rate, the training of overfitting problem with LSTMP RNN architecture with large
LSTM RNNs results in a stable convergence. Apart from clip- number of memory cells (2048) can be seen clearly. We observe
ping the activations of memory cells to range [-50, 50], we do that LSTMP RNN architectures converges faster than LSTM
not limit the activations of other units, the weights or the esti- RNN architectures. It is clear that having more layers helps gen-
mated gradients. eralization but makes training harder and convergence slower.
During training, we evaluate frame accuracies (i.e. phone Table 2 shows how the performance of networks with deep
state labeling accuracy of acoustic frames) on a held-out devel- LSTMP RNN architecture changes with the depth and number
opment set of 200,000 frames. The trained models are eval- of model parameters. We see that increasing the number of pa-
uated in a speech recognition system on a test set of 22,500 rameters over 13M does not improve performance. We can also
hand-transcribed, anonymized utterances. For all the decoding decrease the number of parameters substantially without hurt-
experiments, we use a wide beam to avoid search errors. After a ing performance much. The deep LSTMP RNN architecture
first pass of decoding using the LSTM RNNs with a 5-gram lan- with two layers each with 800 cells and 512 recurrent projec-
guage model heavily pruned to 23 million n-grams, lattices are tion units converges mostly in 48 hours and gives 10.9% WER
rescored using a 5-gram language model with 1 billion n-grams. on the independent test set. Training this model for 100 hours
The input to the LSTM RNNs is log-filterbank energy fea- improves the WER to 10.7% and for 200 hours to 10.5%. In
tures, with no frame stacking. Since the information from comparison, our best DNN models with 85M parameters gives
the future frames helps making better decisions for the current 11.3% at the same beam and training takes a few weeks.
frame, we delay the output HMM state label by 5 frames. We
do not calculate the errors for the first 5 frames of each utter-
ance during backpropagation and we repeat the last frame of Table 2: Experiments with LSTMP RNN architectures.
each utterance for 5 more time steps. C P Depth N WER (%)
1024 512 3L 20M 10.7
4.2. Results 1024 512 2L 15M 10.7
In Table 1, we summarize the results for various LSTM and 800 512 2L 13M 10.7
LSTMP RNN architectures. We observe that the conventional 700 400 2L 10M 10.8
LSTM RNNs with a single layer do not perform very well for 600 350 2L 8M 10.9
this large scale acoustic modeling task. With two layers of
LSTM RNNs, the performance improves but still it is not very
good. The LSTM RNN with five layers approaches the perfor- 5. Conclusions
mance of the best model. We see that training an LSTM RNN
with seven layers is hard, the model starts converging after a We showed that deep LSTM RNN architectures achieve state-
day of training. From the table, one can see that the LSTMP of-the-art performance for large scale acoustic modeling. The
RNN models with a single layer and a large number of memory proposed deep LSTMP RNN architecture outperforms standard
cells tends to overfit the training data. Increasing the number of LSTM networks and DNNs and makes more effective use of the
LSTMP RNN layers seems to alleviate this problem of mem- model parameters by addressing the computational efficiency
orization and to result in better generalization to held-out data. needed for training large networks. We also show for the first
The LSTMP RNN models give slightly better results than the time that LSTM RNN models can be quickly trained using
LSTM RNN model with 5 layers. We see that increasing the ASGD distributed training.
number of parameters in the LSTMP RNN models more than
13M by having more layers or more memory cells does not give
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